Funny that you mention Copernicus whose book on heliocentrism, De revolutionibus orbium coelestium, was placed on the Index of Forbidden Books by a decree of the Sacred Congregation of March 5, 1616:
This Holy Congregation has also learned about the spreading and acceptance by many of the false Pythagorean doctrine, altogether contrary to the Holy Scripture, that the earth moves and the sun is motionless, which is also taught by Nicholaus Copernicus' De revolutionibus orbium coelestium... and by Diego de Zúñiga's In Job ... Therefore, in order that this opinion may not creep any further to the prejudice of Catholic truth, the Congregation has decided that the books by Nicolaus Copernicus [De revolutionibus] and Diego de Zúñiga [In Job] be suspended until corrected.
The book was "corrected", but never reprinted, and therefore remained withdrawn from circulation for 142 *years*. Galileo himself defended Copernicus' work with the church which ultimately ended up with him being found "vehemently suspect of heresy" and held under house arrest for the remaining nine years of his life. In addition all of Galileo's works (present and future) were banned from publication.
I would argue that it's not religious belief that has been a huge help to progress but more the absolute control exerted over people at the time and the financial gains that came from that control that allowed the church to fund education and scientific research - but only as long as it didn't contradict religious beliefs or texts. I.e., the church still held absolute control over what was or was not published. And if that's not a prime example of holding back science, I don't know what is.